To calculate the surface area of the spheres, we can use the formula for the surface area of a sphere, which is:
\[ SA = 4\pi r^2 \]
For Sphere A (radius = 4 inches):
\[ SA_A = 4\pi (4)^2 \] \[ SA_A = 4\pi (16) \] \[ SA_A = 64\pi , \text{in}^2 \]
For Sphere B (radius = 10 inches):
\[ SA_B = 4\pi (10)^2 \] \[ SA_B = 4\pi (100) \] \[ SA_B = 400\pi , \text{in}^2 \]
Comparison of Surface Areas:
- Sphere A has a surface area of \( 64\pi , \text{in}^2 \)
- Sphere B has a surface area of \( 400\pi , \text{in}^2 \)
To find out how many times larger the surface area of sphere B is compared to sphere A: \[ \frac{SA_B}{SA_A} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]
Conclusion:
Sphere A has a surface area of \( 64\pi , \text{in}^2 \) and sphere B has a surface area of \( 400\pi , \text{in}^2 \), meaning sphere B's surface area is 6.25 times as large as sphere A's.